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In the given figure find the ratio of sum of inradius and circumradius for smaller triangle and bigger triangle, if the side of smaller equilateral triangle is 25% of the side of bigger equilateral triangle ?
  • a)
    2 : 3
  • b)
    1 : 4
  • c)
    4 : 7
  • d)
    8 : 3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In the given figure find the ratio of sum of inradius and circumradiu...
Given
Side of smaller equilateral triangle = 25% side of bigger equilateral triangle
Formula used:1) Circumradius = abc/4Δ
2) Inradius = Δ/s
Where, s = (a + b + c)/2
And Δ = Area of triangle
3) Area of equilateral triangle = √3/4 × a2
Calculation:According to question,
Side of smaller equilateral triangle = 25% side of bigger equilateral triangle
Side of smaller equilateral triangle/Side of bigger equilateral triangle = ¼
Sum of circumradius and inradius for smaller triangle,
⇒ 1 × 1 × 1/4 × √3/4 × (1)2 + √3/4 × (1)2/(1 + 1 + 1)/2
⇒ 1/√3 + 1/2√3
⇒ 1/√3 × (1 + 1/2)
⇒ 3/2√3
Similarly,
Sum of circumradius and inradius for bigger triangle,
⇒ 4 × 4 × 4/ 4 × √3/4 × (4)2 + √3/4 × (4)2/ (4 + 4 + 4)/2
⇒ 4/√3 + 2√3/3
⇒ 4/√3 + 2/√3
⇒ 6/√3
Ratio = 3/2√3 : 6√3
⇒ 3/2 : 6
⇒ 3 : 12
⇒ 1 : 4
∴ The correct answer is 1 : 4.
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In the given figure find the ratio of sum of inradius and circumradius for smaller triangle and bigger triangle, if the side of smaller equilateral triangle is 25% of the side of bigger equilateral triangle ?a)2 : 3b)1 : 4c)4 : 7d)8 : 3Correct answer is option 'B'. Can you explain this answer?
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